Finding p-value (z-distribution & t-distribution) EQT 271 Engineering Statistics Maz Jamilah Masnan

Definition 2.6: p-value The p-value is the smallest significance level at which the null hypothesis is rejected.

Example 2.13 (One-Tailed Test) When working properly, a machine that is used to make chips for calculators does not produce more than 4% defective chips. Whenever the machine produces more than 4% defective chips it needs an adjustment. To check if the machine is working properly, the quality control department at the company often takes sample of chips and inspects them to determine if the chips are good or defective. One such random sample of 200 chips taken recently from the production line contained 14 defective chips. Test at the 5% significance level whether or not the machine needs an adjustment.

1.65 0.95 Solution 2.17

P-value = 0.5 – 0.485 =0.015

1.65 0.95 Solution P-value=0.015 2.17

Example 2.12 (Two-Tailed Test)

Solution -1.96 1.96 1.84

P-value = 0.5 – 0.46712 =0.0329

-1.96 1.96 -1.96 1.96 1.84 P-value=2(0.0329)=0.0658

Finding p-value using t-distribution One-tailed-test

Since p-value is between 0.01 and 0.025 which is LESS THAN => Reject

Finding p-value using t-distribution Two-tailed-test

Since p-value is between 0.02 and 0.05 which is LESS THAN => Reject